c编写 Topological Sort

最新推荐文章于 2019-11-23 21:01:20 发布

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最新推荐文章于 2019-11-23 21:01:20 发布

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本文介绍了如何使用C语言编写程序来对有向图进行拓扑排序。拓扑排序的目标是找到图中节点的一种线性顺序，使得对于每条边（u, v），节点u在排序结果中都出现在节点v之前。当图中存在环路时，拓扑排序无法成功。提供的样例程序展示了如何判断输入的有向图，并给出了不同输入下的预期输出。" 8548088,1355392,Android布局居中技巧总结,"['Android开发', '前端开发', '布局技巧']

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Topological Sort

Write a program to find the topological order in a digraph.

Format of functions:

bool TopSort( LGraph Graph, Vertex TopOrder[] );

where LGraph is defined as the following:

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

The topological order is supposed to be stored in TopOrder[] whereTopOrder[i] is the i-th vertex in the resulting sequence. The topological sort cannot be successful if there is a cycle in the graph -- in that caseTopSort must return false; otherwise return true.

Notice that the topological order might not be unique, but the judge's input guarantees the uniqueness of the result.

Sample program of judge:

#include <stdio.h>
#include <stdlib.h>

typedef enum {false, true} bool;
#define MaxVertexNum 10  /* maximum number of vertices */
typedef int Vertex;      /* vertices are numbered from 0 to MaxVertexNum-1 */

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

LGraph ReadG(); /* details omitted */

bool TopSort( LGraph Graph, Vertex TopOrder[] );

int main()
{
    int i;
    Vertex TopOrder[MaxVertexNum];
    LGraph G = ReadG();

    if ( TopSort(G, TopOrder)==true )
        for ( i=0; i<G->Nv; i++ )
            printf("%d ", TopOrder[i]);
    else
        printf("ERROR");
    printf("\n");

    return 0;
}

/* Your function will be put here */

Sample Input 1 (for the graph shown in the figure):

Sample Output 1:

4 3 2 1 0

Sample Input 2 (for the graph shown in the figure):

Sample Output 2:

ERROR

代码如下：

bool TopSort(LGraph Graph,Vertex TopOrder[])
{
	int counter=0;
	int Indegree[MaxVertexNum];
	int queue[MaxVertexNum];
	int head=0,tail=0;
	PtrToAdjVNode node;
	int i=0,j=0;
	for(i=0;i<MaxVertexNum;i++){
		TopOrder[i]=0;
		Indegree[i]=0;
		queue[i]=-1;
	}
	for(i=0;i<Graph->Nv;i++){
		node=Graph->G[i].FirstEdge;
		while(node!=NULL){
			Indegree[node->AdjV]++;
			node=node->Next;
		}
	}
	for(i=0;i<Graph->Nv;i++){
		if(Indegree[i]==0)
			queue[tail++]=i;
	}
	while(head!=tail){
		j=queue[head++];
		TopOrder[counter++]=j;
		node=Graph->G[j].FirstEdge;
		while(node!=NULL){
			Indegree[node->AdjV]--;
			if(Indegree[node->AdjV]==0){
				queue[tail++]=node->AdjV;}
			node=node->Next;
		}
	}
	if(counter!=Graph->Nv)
		return false;
	return true;
}